If there are 2 nlme models with same non-linear mean function, model 1 and model 2, how do you compare them ? Which R function does this for us ?

And when there are random effects or fixed effects, I don't know how a nested model is defined ?

For example model 1,

``model1 <- nlme(df_measures ~ meanfunc(w, time, b0,b1,b2) , fixed = list(b0 ~1, b1 ~ 1, b2 ~ 1), random = b0 + b1 + b2 ~ 1, groups = ~ subject , data = dataa, start = list(fixed = c(b0 = 3,1, b1 = 5,1,b2 = 1,1)), verbose = T )` `

and model 2:

``model2 <- nlme(df_measures ~ meanfunc(w, time, b0,b1,b2) , fixed = list(b0 ~w, b1 ~ w, b2 ~ w), random = b0 + b1 + b2 ~ 1, groups = ~ subject , data = dataa, start = list(fixed = c(b0 = 3,1, b1 = 5,1,b2 = 1,1)), verbose = T )` `

Is model2 a nested model of model 1 ? This is confusing me and how do I compare them ?

If model 2 is a nested model of model 1, can I still use `ANOVA`

function in R to compare them ?

What if model 2 is not a nested model of model 1 ? How should I compare between these 2 models? Based on what criteria ?

Thanks.

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#### Best Answer

Model A is nested within Model B if A is a special case of B. In your example, model 1 is nested within model2 because it equals to the special case of model2, where the slope for `w`

is set to be 0.

My understanding is that the nested nature can apply to both random effects structure and fixed effects structure. Yours is nested in the fixed effect structure. **(edit: in the original post I said "nested in the random effect structure", which is wrong)**

I am not sure about `ANOVA`

, but yes you can use `anova`

to compare them (`anova(model2,model1)`

), although the authors of `nlme`

advise against it, because the likelihood ratio test (for comparing fixed effects) will be anti-conservative. That is, the p-value will be less than what it actually is.

They recommend using the conditional t-test, which is implemented in the `summary`

function. So in your case, there is no need to fit model1, and you can simply look at `summary(model2)`

. The alternative they recommend is the conditional F-test, which is implemented in the `anova`

but with 1 model only. That is, `anova(model2)`

. So you have 2 to choose from.

For completeness sake perhaps I should say that the above advice seems to hold only for fixed effect comparison. If you are making inference on the variance components, then the Likelihood ratio test (from `anova`

) will be conservative instead. But people tend to accept being conservative, which means `anova`

can be used.

My reference is the author's book. Pinheiro & Bates (2000), Mixed-Effects model for S and S-plus

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